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Index of Equivariant Callias-Type Operators and Invariant Metrics of Positive Scalar Curvature

Research paper by Hao Guo

Indexed on: 14 Mar '18Published on: 14 Mar '18Published in: arXiv - Mathematics - Differential Geometry



Abstract

For a Lie group G acting properly and isometrically on a Riemannian manifold M, we define G-Callias-type operators and show they have an index in the K-theory of the maximal group C*-algebra. The construction pairs a Dirac operator with an element of the K-theory of a partial Higson compactification of M; this K-theory is highly non-trivial. The index of such operators is then used to study existence of and obstructions to G-invariant PSC metrics on M.